Question
Download Solution PDFयदि 6x2 + 13x + 7 = 0 के मूल α, β हैं, तब वह समीकरण कौन-सा है, जिसके मूल α2, β2 हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
6x2 + 13x + 7 = 0
प्रयुक्त अवधारणा:
हम जानते हैं कि एक द्विघात समीकरण जिसके मूल α और β हैं, x2 - (α + β) x + αβ = 0 द्वारा दर्शाया जाता है।
गणना:
6x2 + 13x + 7 = 0
⇒ x2 + 13x/6 + 7/6 = 0
इसलिए, (α + β) = - (13/6)
αβ = 7/6
अब,
(α + β)2 = α2 + β2 + 2αβ
⇒ 169/36 = α2 + β2 + 7/3
⇒ 169/36 - 7/3 = α2 + β2
⇒ (169 - 84)/36 = α2 + β2
⇒ 85/36 = α2 + β2
अब,
x2 - (α2 + β2)x + α2β2 = 0
⇒ x2 - 85/36x + 49/36 = 0
⇒ 36x2 - 85x + 49 = 0
∴ अभीष्ट उत्तर 36x2 - 85x + 49 = 0 है।
Last updated on Jul 10, 2025
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